• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.431-445
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• 2015

Extensions of the Kolmogorov convergence criterion and the Marcinkiewicz-Zygmund inequalities from independent random variables to conditional independent ones are derived. As their applications, a conditional version of the Marcinkiewicz-Zygmund strong law of large numbers and a result on convergence in $L^p$ for conditionally independent and conditionally identically distributed random variables are established, respectively.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.1-15
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• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.377-387
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• 2015

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.9
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• pp.143-154
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• 2021

This study aims to explore the dynamic conditional correlation (DCC) between ten Asian stock indexes, the US stock index, and Bitcoin by using the dynamic conditional correlation model. The time span of the daily data is between January 2015 to May 2021, the total observation is 1,116. DCC(1,1)-EGARCH(1,1) with multivariate t and normal distributions for the DCC and EGARCH models, respectively, outperforms other models by the goodness of fit values. Except for Bitcoin, we discovered that the majority of the securities' volatilities have a very high volatility persistence. Furthermore, the negative shocks/news have more impact on the volatilities than positive shocks/news in most of the cases, except the stock index of China and Bitcoin. Most of the correlation pairs exhibit higher correlation during the COVID-19 pandemic compared to the pre-COVID-19, except Hong Kong-The US and Malaysia-Indonesia. Moreover, the correlation between Asian stock indexes during the COVID-19 pandemic is statistically higher than the pre-COVID-19 pandemic. However, there are a few instances where the Hong Kong stock index and a few countries are identical. The result of correlation size shows the connectedness between Asian stock markets, which are well-connected within the region, especially with South Korea, Singapore, and Hong Kong.

• Journal of Korea Water Resources Association
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• v.35 no.1
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• pp.109-124
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• 2002

This study is an effort to develop a stochastic model of precipitation series that preserves the pattern of occurrence of precipitation events throughout the year as well as several characteristics of the duration, amount, and intensity of precipitation events. In this study an event cluster model is used to describe the occurrence of precipitation events. A logarithmic negative mixture distribution is used to describe event duration and separation. The number of events within each cluster is also described by the Poisson cluster process. The duration of each event within a cluster and the separation of events within a single cluster are described by a logarithmic negative mixture distribution. The stochastic model for hourly precipitation occurrence process is fitted to historical precipitation data by estimating the model parameters. To allow for seasonal variations in the precipitation process, the model parameters are estimated separately for each month. an analysis of thirty-four years of historical and simulated hourly precipitation data for Seoul indicates that the stochastic model preserves many features of historical precipitation. The seasonal variations in number of precipitation events in each month for the historical and simulated data are also approximately identical. The marginal distributions for event characteristics for the historical and simulated data were similar. The conditional distributions for event characteristics for the historical and simulated data showed in general good agreement with each other.

• Journal of information and communication convergence engineering
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• v.19 no.4
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• pp.228-233
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• 2021

In this study, we analyze the credit information (loan, delinquency information, etc.) of individual business owners to generate voluminous training data to establish a bankruptcy prediction model through a partial synthetic training technique. Furthermore, we evaluate the prediction performance of the newly generated data compared to the actual data. When using conditional tabular generative adversarial networks (CTGAN)-based training data generated by the experimental results (a logistic regression task), the recall is improved by 1.75 times compared to that obtained using the actual data. The probability that both the actual and generated data are sampled over an identical distribution is verified to be much higher than 80%. Providing artificial intelligence training data through data synthesis in the fields of credit rating and default risk prediction of individual businesses, which have not been relatively active in research, promotes further in-depth research efforts focused on utilizing such methods.

• Journal of Korea Water Resources Association
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• v.35 no.6
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• pp.763-777
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• 2002

The objective of this study is to develop computer simulation model that produces precipitation patterns from stochastic model. The hourly precipitation process consists of the precipitation occurrence and precipitation amounts. In this study, an event cluster model developed by Lee and Lee(2002) is used to describe the occurrence process of events, and the hourly precipitation amounts within each event is described by a nonstationary form of a first-order autoregressive process. The complete stochastic model for hourly precipitation is fitted to historical precipitation data by estimating the model parameters. An analysis of historical and simulated hourly precipitation data for Seoul indicates that the stochastic model preserves many of the features of historical precipitation. The autocorrelation coefficients of the historical and simulated data are nearly identical except for lags more than about 3 hours. The precipitation intensity, duration, marginal distributions, and conditional distributions for event characteristics for the historical and simulated data showed in general good agreement with each other.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.71-87
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• 2014

The Bayes premium or the net premium in the credibility theory does not reflect the underlying tail risk. In this study we examine how the tail risk measures can be utilized in determining the risk premium. First, we show that the risk measures can not only provide the proper risk loading, but also allow the insurer to avoid the wrong decision made with the Bayesian premium alone. Second, it is illustrated that the rank of the tail thickness among different conditional loss distributions does not preserve for the corresponding predictive distributions, even if they share the identical prior variable. The implication of this result is that the risk loading for a contract should be based on the risk measure of the predictive loss distribution not the conditional one.